The explicit generalized-\(\alpha \)  method, at each time step, factors the isogeometric mass matrix; thus, we use a preconditioned conjugate gradients (PCG) as an iterative solver using \(\mathcal {M}\)  [1]}, which is easy to implement, extremely efficient and robust. We build the preconditioner using a diagonal scaling of the parametric mass matrix (i.e., matrix associated with the \(d\) -dimensional cube pre-image of the parametric space) for single-patch geometries. We combine the preconditioners defined above for each patch for multi-patch geometries using an additive Schwarz domain-decomposition method. In [1]}, the authors proved that these preconditioners are efficient to apply and are robust with respect to the mesh size; in the single-patch case, they show that the behaviour improves as the problem size grows (mesh refinement).
